Investigating Two Methods of Teaching Mathematics Based on Work Mathematics and Understanding Mathematics Included in the General Mathematics

The didactics of mathematics, as well as the process of learning this subject, are considered fundamental components within the curriculum of educational institutions worldwide, spanning from primary schools to universities. Nations that prioritize and support mathematics education allocate substantial resources towards this endeavor. The primary objective of this article is to conduct an in-depth analysis of two distinct methodologies for imparting mathematical knowledge, specifically tailored for the general mathematics course.

To fulfill this objective, we commenced by elucidating the fundamental concepts underpinning the process of learning, delving into its historical context, followed by an exploration of diverse definitions associated with learning phenomena.

Within our discourse, we delved into the realm of conditional learning, shedding light on the aspect of knowledge retention and the potential obstacles that may hinder the permanence of acquired knowledge. Furthermore, we elucidated the concept of learning through the analogy of two distinct pulses, each consisting of two intricate stages. The initial pulse revolves around the challenges and limitations encountered in the learning process, while the subsequent pulse focuses on the enhancement and development of one's cognitive capacity. These stages were meticulously employed in the pedagogical approach to teaching mathematics, accompanied by illustrative examples to elucidate each facet of the learning process.

Subsequently, a critical analysis of different pedagogical strategies in mathematics education was undertaken. Two distinctive approaches for teaching general mathematics (course 1) to engineering students were proposed:1. Instruction through active mathematical problem-solving. 2. Instruction emphasizing conceptual understanding in mathematics.